Simultaneous linear equations: CJC 2024 Promo Q1

When $x=1$, $$\begin{aligned} 0&=p(1)+\sqrt q-\ln(r)\\ p+\sqrt q-\ln r&=0\quad\text{-------- (1)} \end{aligned}$$ When $x=2$, $$\begin{aligned} 0&=p(2)+\sqrt{2q}-\ln(2r)\\ 2p+\sqrt2\sqrt q-\ln r&=\ln2\quad\text{-------- (2)} \end{aligned}$$ When $x=5$, $$\begin{aligned} 0&=p(5)+\sqrt{5q}-\ln(5r)\\ 5p+\sqrt5\sqrt q-\ln r&=\ln5\quad\text{-------- (3)} \end{aligned}$$ Using G.C., $$\begin{aligned} p&=-0.4518351361\approx-0.452\quad\text{(to 3 d.p.)}\\ \sqrt q&=2.764231837\ \Rightarrow\ q=2.764231837^2=7.640977649\approx7.641\quad\text{(to 3 d.p.)}\\ \ln r&=2.312396701\ \Rightarrow\ r=\mathrm{e}^{2.312396701}=10.098599\approx10.099\quad\text{(to 3 d.p.)} \end{aligned}$$